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Hard Boiled Egg

Posted by Karl Sharman on June 19, 2010 – 8:19 am

Something nice and easy for the weekend….

You are the worlds finest chef, currently working at the finest restaurant in Puzzlaria.

One December morning after a particularly heavy snow storm, the power fails. Fortunately, there is still an old wood stove with which you can prepare most of the meals. However one cantankerous customer, Zaux, has a peculiar item which now poses a problem. He likes a single egg boiled for exactly nine minutes.

You aren’t wearing your watch, and all the clocks in the building are electric. You are able to find two exquisite hourglasses, able to pricely measure in (hand-crafted swiss) sand seven and four minutes, respectively.

How quickly using only these two hourglasses can you provide Zaux with his egg?


This post is under “MathsChallenge” and has 30 respond so far.
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30 Responds so far- Add one»

  1. 1. Joe Said:

    ~solution alert~ :

    14 minutes

    how i did it:
    first turn both until the 4 minute one ends
    then turn it over and boil the egg until the 7 minute one ends
    then stop boiling egg and turn over 7 minute one
    after 4 minute one ends boil egg again until 7 minute one ends

    14 minutes have past, and the egg was boiled for 9 minutes, there you go

  2. 2. Karys Said:

    Return the 4mn and 7mn at the same time.

    4 mn later, return the empty 4mn.

    3 mn later (7mn total), return the 7mn, there is one minute left in the 4mn hourglass.

    1 mn later return the 7 mn hourglass, where 1 mn passed.

    1mn later, 7 is empty.

    Total of 9 minutes.

  3. 3. killmenow5000 Said:

    turn over 7min hour glass
    when it runs out turn over the 4min hour glass when half the sand is in the bottom the egg is done
    simple compared to other answer

  4. 4. Gary Holmes Said:

    Karys is too smart. The answer seems 2b right?

    Cautions:

    1) When turning an HourGlass, need to do it instantly, without losing any time-gap.

    2) Or, precisely calculate time-required for turning, hence turn it in advance.

    3) Initially, use both hands for 2 HourGlasses, plus a 3rd hand to start boiling egg — All started concurrently.

    Without 3rd hand, maybe using teeth would help…?

    4) Toward the end, quickly remove egg from boiling water. Instantly rinse under cold water, within a split second. Otherwise, the residual heat will continue cooking the egg.

    5) Karl, does it matter whether it’s a Medium or Jumbo egg?

    6) Karys, how to see the last grain of sand dropping? Maybe a candle behind ea HourGlass would help?

    Gary Holmes

  5. 5. Benjamin Said:

    Stopwatch on your mobile phone
    Ben Mccluskie

  6. 6. Seth Said:

    How Quickly? Hmmmm… Well if it is to be “Exactly” what he ordered, then I guess 9 minutes.

  7. 7. Quaid Said:

    1) It’s the world’s finest restaurant, so obviously you wont be the only chef over there. There are other chef’s too.

    2) You aren’t wearing your wrist watch doesn’t means other too are not wearing their wrist watches.

    3) Better use a wrist watch from your colleague, boil the egg for 9 minutes and serve it to Zaux.

    HourGlasses only look better in PRINCE OF PERSIA and not such puzzles. ;)

    I hope this was a logical puzzle and considering that my answer is correct. ;)

  8. 8. kapakoi Said:

    No, no, no, no time gaps when boiling an egg. It keeps cooking as long as its temp. is ~60 degrees and above. So you need to prepare the 7 min hourglass (HG7) to have 2 minutes left in it.
    1) turn HG4 and HG7 at the same time
    2) HG4 runs empty, turn it while HG7 still running
    3) HG7 runs empty, HG4 has 1 minute in it. Turn both
    4) HG4 runs empty, HG7 has 6 minutes, turn HG4
    5) HG4 runs empty, HG7 has 2 minutes, throw the egg into boiling water!
    6) HG7 runs empty, turn it, and cook the egg until HG runs empty

    so HG7 gets to run through 3 times and 21 minutes for all process

  9. 9. Shawn Said:

    Zaux is just going to have to get used to not getting his way. Use the seven minute hour glass, when it stops turn the 4 minute hour glass over. When the four minute hour glass is finished, give Zaux his damned eggs. Or you could just get the eggs off the heat source after the 7 minute hour glass is done followed by half the 4 minute hour glass if you subscribe to the stupid saying of “The customer is always right”.

  10. 10. mkcdcf Said:

    Run the 7 min timer, then guesstimate half way through the 4 min timer to approximate 9 min as close as possible.

  11. 11. Gary Holmes Said:

    1) Kapakoi seems 2b the smartest.

    2) I think Kapakoi has been a chef b4.
    * His idea doesn’t present any worry about time-gap.
    * He suggested to boil water 1st, so that chef doesn’t waste time for increasong the temp from 60F to 212F.

    3) But, we all have been tricked by Karl — again:
    * World’s finest restaurant does not serve boiled eggs.
    * Pizzalia only serves pizza.
    * High-class restaurants dont open until 5pm, not Dec morning…

    4) Zaux needs 2b executed by Ragknot, for stringent appetize.

    Gary Holmes

  12. 12. BootieHandler Said:

    1) turn HG4 and HG7 at the same time
    2) HG4 runs empty, turn it while HG7 still running, HG7 has 3 minutes left
    3) HG7 runs empty, HG4 has 1 minute left in it, throw the egg into boiling water!
    4) Put HG7 away, it is no longer used.
    5) HG4 runs empty, egg has 1 minute on it, turn HG4,
    6) HG4 runs empty, egg has 5 minutes on it, turn HG4 again,
    7) When HG4 runs empty the egg has cooked continuously for 9 minutes

    9 minutes cooking time + 7 minutes preparation = 16 minutes

  13. 13. Euclid's Brother Said:

    Get the water boiling first.
    Put in the egg & Start both hourglasses.
    When the 4 min runs out, flip it. (4 min elapsed)
    When the 7 min runs out, flip it. (7 min elapsed)
    When the 4 min runs out, flip 7 min hg. (8 min elapsed)
    When the 7 min runs out, egg is finished (9 min elapsed)

    Serve hot.

  14. 14. Euclid's Brother Said:

    Oh.. Total time after getting water to boil is still only 9 mins.

  15. 15. OldGoaltender Said:

    Boil water.
    Start HG4 and HG7.
    When HG4 runs out HG7 has 3 minutes to go.
    Start HG4 again.
    When HG7 runs out HG4 has 1 minute to go.
    Put egg in water.
    When HG4 runs out start HG4 again.
    When HG4 runs out egg has boiled for 5 minutes.
    Start HG4 again.
    When HG4 runs out egg has boiled for 9 minutes.
    Take egg out of the boiling water.
    Total elapsed time is 16 minutes.

  16. 16. Chris Said:

    ??? Karys gave the best possible time in the second post. Why are folks giving poorer solutions?

  17. 17. pramsay13 Said:

    ^ maybe because there are better solutions… and Euclid’s brother has it.

  18. 18. Karl Sharman Said:

    The question asks how quickly can you boil a nine minute egg, given 2 x hourglasses with a 4 and 7 minute timescale.

    Many worked out that you could use the timers to boil an egg for nine minutes, in nine minutes.

    Karys came in first, with Seth coming in with the obvious answer….

  19. 19. BootieHandler Said:

    RE: Euclid’s Brother

    >When the 4 min runs out, flip 7 min hg. (8 min elapsed)
    >When the 7 min runs out, egg is finished (9 min elapsed)

    At the eight minute mark, HG7 is flipped with 7 minutes left on it. When HG7 runs out it is 7 minutes later, not 1.
    8 + 7 = 1? How?

    RE: Chris
    >??? Karys gave the best possible time in the second post. Why are folks giving poorer solutions?

    Answer? Because Kary is wrong.

    min. mark HG4 mins HG7 mins
    0 4 7
    4 0(flip)4 3
    7 1 0(flip)7
    8 0 6(flip)7

    7 minutes into this hg7 is turned, with 7 minutes left on it. 7+7=14
    8 minutes into this hg7 is turned, with 7 minutes left on it. 8+7=14
    1mn later, 7 is empty? Not possible.

    At the core, 9 is not divisible by 7 or 4, 9 minutes is not a possibility.

    RE: Karl Sharman

    >Many worked out that you could use the timers to boil an egg for nine minutes, in nine minutes.
    This is incorrect therfore => ‘Karys came in first, with Seth coming in with the obvious answer….’ is also False

  20. 20. Chris Said:

    BootieHandler – Karys and EuclidsBrother are both right.

    Start with both zeroed, turn both. After 4 mins HG4 is empty and HG7 has 3 minutes left (4 minus so far). Flip HG4. When HG 7 finishes (7 minute so far), there’s 1 min left in HG4. Flip HG7 (which is now has 7 mins worth of sand). When HG4 has finished (1 min later, 8 minutes so far) HG 7 will have 1 minutes worth of sand used. Flip HG7 which now runs for the final 1 minute, bringing us to 9 minutes as rquired.

    “At the core, 9 is not divisible by 7 or 4, 9 minutes is not a possibility” – I cannot imagine why you think that matters.

    What matters is that 4 + (4-(7-4)) + 1 = 9, the 1 being a copy of (4-(7-4)).

  21. 21. Chris Said:

    Oooops. I messed up the last “equation”. It should have implied 4 + 3 + 1 + 1 = 9.

    The 3 is from 7-4. The first 1 is from 4-3 and is measured by HG4, and the second 1 is simply a copy of the 1 and is measured by HG7.

  22. 22. BootieHandler Said:

    Chris, I don’t know what to tell you? Unfortunately I see this crystal clear and I persist that I am right and I can explain exactly how I am right. I still persist the ‘the core’ is just that. This is the one logical statement that proves that a total elapsed time of 9 minutes total cannot occur, ever. If the hourglasses where 2 minutes and 7 minutes or 1 minute and 8 minutes or 3 minutes and 6 minutes or 5 minutes and 4 minutes, I’m with you. But, since they are not, you cannot come to the 9 minutes cooking time without some preparation time. Since this is the case, any amount of time (time>0), makes the total time necessary before the eggs is done more than 9 minutes, which in turn makes the claim that the cooked egg can come out after only 9 minutes, false. It is not physically possible in this world with those two timers. The strategy is what combination yields the least amount of prep time. For those who understood the question, the best answer so far was 23 minutes. At a glance that seemed a bit high to me. So working backwards:
    to achieve 9 minutes you can use: 7 is 2 minutes short, 7 and 4 is two minutes to long (11 mins), 4 minutes twice is one minute short. I need to make up the 1 minute or two minutes, either will work. I can make up this 1 by starting the 4 minute and 7 minute at the same time and flipping the 4 when it runs empty. I have my exact one minute of sand but it took 7 minutes to get there.
    These statements do not posses sound mathematical logic.
    ” When HG 7 finishes (7 minute so far)…Flip HG7 (which is now has 7 mins worth of sand)”=> 14 minutes by my count.
    “Flip HG7 which now runs for the final 1 minute”… and an additional 6 minutes. HG7 was just flipped, it has 7 minutes left, not one.

  23. 23. Joe User Said:

    RE: Chris Said:
    June 24th, 2010 at 11:46 am

    HG7 was turned over 3 times after running empty. That is 21 minutes! I’m glad you aren’t my cook.

    “It is not wise to try to teach a bird math, it only serves to frustrate you and anger the bird” – unknown

  24. 24. Euclid's Brother Said:

    Bootie Handler… Let see if I can make this CRYSTAL CLEAR for you.

    Both HG start out at the top.. 7min for the 7min hourglass and 4 min for the 4 min hourglass.

    Put the egg in and flip both HG’s.

    When the 4 min runs out, flip it over to start again. Now the current state: 7min hg has 3 mins left. and 4min has 4min again. (Total time elapsed 4 mins)

    When the 7 min runs out, flip it over to start again. Now the current state is: 7 min hg has 7 mins left and 4 min has 1 min left. This is because the 4 min stated when the 7min had only 3 mins left. (Total time elapsed 7 mins)

    When the 4 min runs out, flip the 7 min hour glass. Now the current state is: 7 min hg has 1 min left. Since the 4 min had only 1 min left, then when it ran out, the 7min still had 6 mins left. So after the flip it had 1 min left. (Total time elasped 8 mins)

    So now when the 7 min runs out (which had only 1 min time left), then the egg is done. (9 mins total elapsed.

    Your mistake is in this line:

    ” When HG 7 finishes (7 minute so far)…Flip HG7 (which is now has 7 mins worth of sand)”=> 14 minutes by my count.

    Yes. after this flip, the 7min has 7 mins left. But it will get flipped again in 1 min, when the 4min runs out. So when the 7 min has 6 mins left, it will get flipped and only have 1 min left.

    Don’t make me call my brother!!!

  25. 25. Chris Said:

    BootieHandler. When HG7 has run down, and you turn it over for 1 minute (timed from HG4) (it now has 1 min of sand at the bottom and 6 mins at the top), you then turn HG7 over again (you don’t wait for it to do the entire 7 minutes), it will only have 1 minutes worth of sand to drop.

    Of course the solution assumes that the hourglass drops sand at a constant rate (constant number of grains of sand per second).

    The problem is about addition and subtraction, not multiplication. Why do you think multiplication is at the core – (the assertion is completely beyond me)? Why does your solution bypass the divisibilty criterion?

  26. 26. Chris Said:

    Hi Joe User. Yes, HG7 was turned over 3 times. Once for 7 minutes, once for one minute (leaving 6 mins at the top) and once more for 1 minute (starting with 1 minutes worth of sand), that’s 9 minutes, not 21.

  27. 27. Chris Said:

    Hi BootieHandler, IF you have realised that Karys and EB have a valid solution, you’ll also have to accept that your divisibility criterion is complete nonsense and not even remotely logical.

    For your own sake you should attempt to identify what properties of the system should be multiplied together and what the physical meaning of that product is?

  28. 28. BootieHandler Said:

    Chris, I see what you are talking about now!!! For some reason I had it in my head that when the hourglass was flipped, it was reset. A hourglass always resets itself to full value (just not immediately). Here is what clarified it ‘(it now has 1 min of sand at the bottom and 6 mins at the top)’.

    It is so hard to get my head out of digital and back into analog… Thanks guys.

  29. 29. Chris Said:

    Hi BootieHandler. Phew! ;)

  30. 30. xxZEROxx Said:

    Turn over the 4 min hourglass. In that time boil the water. When it runs out, put the egg in. When the customer complains after 13 minutes that his egg is being overcooked, it WILL be exactly 9 minutes that the egg was cooked. :)

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